Find the greatest 4 digits number which when divided by 18,24,30 and 36 leaves a remainder 17 (in each case).

- anonymous

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- amoodarya

a=18q+17
a=24k+17
a=30p+17
so
30|a-17
24|a-17
18|a-17
so
[24,18,30]|a-17

- anonymous

I need a way by which I can calculate answer to such question in 1-2 mins time. This type of questions appears in admission exam for MS(CS).

- anonymous

no offense but @amoodarya I got no clue what you did back there. A little explanation please ?

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## More answers

- UsukiDoll

that notation for the second one is 30 divides a -17
similarly 24 divides a-17 and 18 divides 1-17

- ganeshie8

Let \(a\) = required number
Notice that \(a-17\) is divisible by each of the given integers, therefore \(a-17\) must also be divisible by their lcm, \(360\) :
\[a-17 = 360k\]

- amoodarya

[30,24,18]=[5.3.2, 2.2.2.3, 3.3.2]=2.2.2.3.3.5=\[2^3*3^2*5=360\\a-17=360k\\a=360k+17\\a_\min=360*3+17=1080+17\]

- anonymous

@ganeshie8 and others thank you!

- UsukiDoll

when did k =3 for the last line? just wondering. unless we have k = 3 because it's the lcm of 18,24,30, and 36.

- anonymous

Lol I think @amoodarya assumed k = 3 :P

- UsukiDoll

:S there is always a reason to let k = 3. isn't it?

- anonymous

I can't think of any reasons to do so :| cause 3 isn't given in the question

- UsukiDoll

the only thing I can think of is that 3 is the lcm of 18.24.30.36.. not to mention that's part of the 3 x table
3 x 6 =18
3 x 8 = 24
3 x 10 = 30
3 x 12 = 36
3 x 3 x 2 = 18
3 x 2 x 2 x 2 = 24
3 x 2 x 5 = 30
3 x 3 x 2 x 2
Each of them has at least 1 3

- anonymous

yup thats true

- anonymous

@amoodarya it'll be less confusing if you just type down a few words explaining the problem like ganeshie8 did. Thanks

- amoodarya

\[a=360k+17 \ge 1000\\360k \ge 1000-17\\k \ge \frac{1000-17}{360}\\k \space is \space integer \\k \ge 3\]

- UsukiDoll

where did you get the 1000 from?

- anonymous

largest 4 digit number is 9999
Man Imma cry now seriously

- anonymous

@amoodarya you're not helping sir rather you are making it more confusing and complex :|

- UsukiDoll

yeah this is how my adviser would do... just be like ok this this this the end.

- anonymous

LOL I hate such kind of teachers >:|
Teacher's job is to explain the whole process....

- UsukiDoll

yeah I got a B- for absolutely knowing 5.5 out of 8 chapters in Passage to Advanced Mathematics book

- amoodarya

oh . sorry
i had a little mistake
i wrote it for smallest 4 digits
so you do it for the greatest , like that

- anonymous

@ganeshie8 can you make things simple its seriously frying my brain :|

- UsukiDoll

wow I wish my retired professor was on here. He was awesome.

- ganeshie8

spoonfeeding is not good always, it would be more fun if you try and solve the problem on your own based on the given hints

- amoodarya

\[a \leq 9999\\360k+17 \leq 9999\\k \leq \frac{9999-17}{360}\]

- UsukiDoll

well what if the person made so many attempts and then got fed up?

- ganeshie8

where are the "many" attempts ?

- anonymous

^ yes that's what I am doing for last 1 hour :|

- UsukiDoll

k is less than or equal to 27.7222222222 something seems legit

- UsukiDoll

"many" attempts? lol like using every theorem out there

- ganeshie8

teaching is not easy... there is no way for a teacher to know what the student has already tried right

- UsukiDoll

showing off like what my professor did to me a while back doesn't help me understand either -_-

- anonymous

^

- ganeshie8

try this :
teach me how to multiply 3*5

- UsukiDoll

ummm let's see. it's like writing 3 5 times and adding them up

- anonymous

3*5 = 15 simple enough :O

- ganeshie8

how do you know i know addition ?

- UsukiDoll

omg! take 3 rocks that's 1 batch
then 3 rocks 3 rocks 3 rocks 3 rocks... add them all up

- anonymous

alright I'll solve it myself .... no more arguments

- ganeshie8

where do i find rocks ?
your explanation is confusing me

- UsukiDoll

you find rocks outside!

- amoodarya

|dw:1435484624755:dw|

- UsukiDoll

or buy them or find them at a park or at your house

- ganeshie8

now that i don't want to buy rocks, why do i need rocks ? how are they related to multiplications

- anonymous

OMG thats childish @ganeshie8 :|
@amoodarya 's work was confusing me because he took the question wrongly.

- UsukiDoll

don't want to buy rocks ! BORROW MARBLES FROM YOUR FRIEND!

- anonymous

I'm outta here seriously....

- ganeshie8

so i need to have a friend to understand multiplcations ?

- UsukiDoll

-_-! you have none.. draw circles on paper.

- ganeshie8

Okay enough, we're not getting anywhere. I hate math and you're the reason for that.

- UsukiDoll

wow... then you as a student fail then

- ganeshie8

isn't that obvious

- UsukiDoll

*rolls eyes* why waste my time with gibberish? If you still don't understand it after so many tries, it becomes useless to the point that the only way to solve this issue to just fail the student and send it to summer school.

- ganeshie8

same thing can repeat in summer school

- UsukiDoll

then why should the student still be in school then? Have it kicked out of the system and force it to get a job.

- ganeshie8

more or less, thats the story of most school dropout these days right
one bad/annoying teacher is all it takes

- UsukiDoll

not the teacher's fault really. It's the student. If they are not committed...don't bother... just do something productive with life and that's it.

- ganeshie8

you(teacher) failed to teach me(3rd grade kid) how to multiply

- UsukiDoll

-_-! No you failed yourself.

- ganeshie8

more than that, you killed my confidence and love of math

- UsukiDoll

and you have gotten really annoying after a while.

- ganeshie8

hmm

- UsukiDoll

annas and amoodarya got it right. It was just you !

- ganeshie8

aren't we role modeling anymore, you as a good teacher and me as a poor student ?

- UsukiDoll

KNOCK IT OFF ALREADY!

- ganeshie8

Okay fine

- UsukiDoll

and it's role playing...

- anonymous

It's a fault on both ends
cause our teachers now a days are not as determined as they used to be in 90's
and our students shows no seriousness in studies. Well it is kind of a fault of teachers, a good teacher always try to develop interest of his/her students in the subject. Our education system is faulty and teacher's only see teaching as a profession and nothing else.... Sad story!

- UsukiDoll

geez... this is not helping annas at ALL! What started out as trying to clarify things turned into stupid stuff that is NONSENSE AND OFF TOPIC!

- ganeshie8

I agree annas, its always the fault of teacher.

- UsukiDoll

what about favoritism?

- anonymous

@ganeshie8 I am not a 2 year old to be spoon feed I know maths very well... Only problem is I dont remember basic stuff cause of lack of practice. And I am doing this basic stuff just for a stupid test for admission in MS. I've an interview related to my field i.e. software engineering but to qualify for that I need to clear this stupid test... The only reason to ask this question...

- UsukiDoll

that's it... @Michele_Laino Help :*(

- anonymous

Favoritism is another issue in our education system... Teachers give marks for free to those students that they think are most favorite... It's a flaw of teacher AGAIN. I hate this current education system.

- ganeshie8

i think we're done with the original main q ?

- anonymous

Oh I solved the question on my own thank you @UsukiDoll
answer I got was 9989.
@ganeshie8 I didnt start all this discussion all I was asking is for some clarification.

- ganeshie8

9989 is wrong
are you still looking for clarification ? what part do you not understand in ammodarya's solution ?

- UsukiDoll

@annas I know a good example that happened at my university
remembered that annoying professor I had for that Intro to Advanced Mathematics class?
he gave me a B- which was surprising because like I said I only mastered 5.5 out of 8 chapters. Fast forward to a year later... some girl had the same professor and ended up almost failing like a D-
Keep in mind that annoying professor happens to be my undergrad. adviser.

- ganeshie8

\(a = 360k+17\)
Is it hard to solve \(k\) that gives the maximum \(4\) digit number ?

- anonymous

I was taking k = 27.7 now I took k = 27 and I got 9737

- ganeshie8

thats looks correct

- anonymous

Alright, thanks

- ganeshie8

yw, the dicussion was not so fruitful but i enjoyed it thanks!

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